In order to address the problems created by the strong
linear correlation of Figure Five I examined the data of Table II more
rigorously.

I noted that the spread of individual side deviations from
the respective pyramid mean always seemed to follow certain patterns.
For example, I ranked the absolute values regardless of geographical side or
sign. That is, for Meydum they were 21.00, 12.00 8.30, and 1.40. The
values for the Bent Wall were 11.00, 5.40, 3.70, and 2.00. Since Figure Five
shows that the magnitude of the respective pyramid deviations were dependent
on their sequence in the total project, I calculated the ratio of the
individual deviations to the mean for each structure. This normalized
the deviations, or put them on equal footing to permit more rigorous
evaluation. I show these normalized results in the following table.

TABLE IIINormalized Side Deviations in Parts/10,000

Pyramid

MeanDeviation

N

E

S

W

Meydum

10.70

-0.78

+1.96

-0.13

-1.12

Bent Wall

5.50

-0.67

-0.98

-0.36

+2.00

Giza 2

1.70

-2.06

+0.22

+1.41

+0.41

Giza 1 Core

1.20

+0.77

-1.92

+0.21

+0.92

Giza 1 Case (P)

0.72

+0.90

-1.67

+1.08

-0.31

Giza 1 Case (C)

2.40

-1.80

-0.18

+1.88

+0.26

If we now take these calculated values and rank them by
numerical magnitude we obtain the following:

TABLE IVNormalized Side Deviations Ranked by Magnitude

Pyramid

LargestDeviationSide

2nd

3rd

SmallestDeviationSide

Meydum

1.96

1.12

0.78

0.13

Bent Wall

2.00

0.98

0.67

0.36

Giza 2

2.06

1.41

0.41

0.22

Giza 1 Core

1.92

0.92

0.77

0.21

Giza 1 Case

1.67

1.08

0.90

0.31

ArithmeticAverage

1.92

1.10

0.71

0.25

Cole Case

1.88

1.80

0.26

0.18

I show Cole’s Case values separately because we have now
established that his measurements do not possess the refinement necessary to
become part of this study.

A brief look at the last table quickly reveals another
startling result. The normalized values of the side deviations with
respect to the mean, without regard to sign or side, show that the values for
the individual pyramids are very close to one another in the respective
columns. The largest normalized side deviations are spread from 1.67 to
2.06. The second largest deviations are spread from 0.98 to 1.41.
The next two columns show a continuing monotonic decrease indicated by the
mean values.This means that the designer/builder predetermined how the
side deviations of each structure would vary in magnitude, but not with
respect to side or sign of the difference from the deviation mean.

If we plot the mean values, while showing the range among
the five structures, we obtain the following.

The open circles are the arithmetic means for the five
structures. The vertical lines and bars show the spread in values. The closed
diamond shows Cole’s values for Giza 1 case.

Once again we have an amazing arrangement of data,
dramatically illustrated by graphical plot.

We can easily recognize that the variation by side, when
plotted against the side number, shows a linear correlation relationship. The
calculated regression line has an intercept at a normalized 2.35 parts/10,000
and a slope of -0.54 parts/10,000 per side.To further enhance his mathematical finesse the designer used
values which again show neat numbers. When I calculated the regression
line I found that the average X value was 2.5 and the average Y value was 1.0.

The designer not only knew linear graphical relationships,
including exponential and logarithmic forms — he also knew what it meant to
normalize data, and to reduce them to a common reference.

In order to achieve such relationships the designer had to
know in advance the methods of each structure. He designed Meydum to be
larger in deviation, and Giza 1 to be far closer. But he did so in such a way
that the normalized values would fit neatly in relationship as shown on Figure
Six. In other words, he calculated the deviations to be related to the amount
of geographical misalignment while relating them also to one another strictly
on the basis of deviation. Meydum had the largest which, on an absolute
scale would not appear related to the other pyramids, while on a normalized
scale readily shows that relationship.

Figures Five and Six now show explicitly that Meydum was
intended to be part of the overall pyramid project. It does not sit in
isolation, related merely by chance as one might claim from Figures One and
Two.

We also can see that the side deviations of the Menkaure
pyramid violates this scheme, and cannot be included on the last two Figures.
It was not intended to be part of the geometric project.

We see further that Cole’s measurements come into
increasing question. His values do not fit neatly on Figure Six. The second
and third sides are respectively far too high and too low. This fact
reinforces our respect for the superb measurements of Flinders Petrie, who
stands out above other men. Petrie was equal to the original designer in
his measurements; Cole was not.The remaining casing stones found at Meydum may have been
intended to provide data to tie that structure to the other 4th dynasty
pyramids without ever having been completed. At some point, work on the
outer casing was suspended because it was no longer necessary.

The data of Figure Six might help us understand the range
of errors, either in the construction, or in our measurements. I reviewed the
maximum and minimum values for each side as shown in Table IV. I learned that
of the eight limits on the Figure were due to the two Giza pyramids. The
median points also were populated by the Giza pyramids. This merely
tells us that the greatest errors took place where the requirements were the
tightest. Since the constructions test our modern measurement abilities
we cannot say from these numbers if the spread in data is due to the former or
the latter.

One is tempted to “force” the averages to some
numerical clean value, such as 2.00 at side 1, 1.25 at side 2, and so on, with
a slope of -5.0, to obtain neater regression points, but I could find no clear
fit that would justify such manipulation of the numbers. The designer offered
us striking information without resorting to such artificial values.